Recently, interest has appeared in inverse spectral problems for differential operators on closed sets, see [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. Such problems consist in recovering operators from their spectral characteristics. The most complete results in this direction were obtained for the classical Sturm–Liouville operator on an interval, see [8]}, [9]}, [10]}.
Posing and studying inverse problems substantially depend on the structure of the considered closed set, which leads to the need for some or other restrictions.
By the present time, the most general form of the sets on which the solution of an inverse problem has been obtained is a finite union of segments and isolated points, see [5]}, [7]}.
